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If n is an integer between 10 and 99, is n < 80?
(1) The sum of the two digits of n is a prime number.
(2) Each of the two digits of n is a prime number.
(1) The sum of the two digits of n is a prime number.
(2) Each of the two digits of n is a prime number.
I know this must be easy. The answer is B (statement 2 is sufficient alone, while statement 1 is not). Doesn't that lead to tons of possible values of n?
vandygrad11
If n is an integer between 10 and 99. Is n < 80?
Notice that n is an integer between 10 and 99 means that n is two-digit integer.
(1) The sum of the two digits of n is a prime number. Clearly insufficient: for example 83>80 and 38<80.
(2) Each of the two digits of n is a prime number --> greatest one digit prime is 7, thus max value of n is 77, which is less than 80. Sufficient.
Answer: B.
vandygrad11
We are told that n is a two-digit integer and each of these two digits is a prime, so n can be: 22, 23, 25, 27, ... and as greatest one digit prime is 7, thus max value of n is 77.
As what n could be taking in account statement (1):
23 --> 2+3=5=prime;
25 --> 2+5=7=prime;
29 --> 2+9=11=prime;
...
Hope it's clear.
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vandygrad11
1. let n be 67 then 6+7 = 13 (prime) and n < 80
but if n is 89 then 8+9 =17 (prime) and n >80. hence insuff
2. 8 and 9 are not prime so n < 80 as no value above 80 satisfies stmnt 2
hence suff
B
General Discussion
kp1811
I am lost on this one. Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, etc. There are several values that satisfy the conditions of 10>n>80 while both digits are prime numbers, for instance 23, 32, 57, etc. Is that the reason that we can eliminate #2? Similarly, not to sound stupid, but is 67 then the only integer that meets the conditions of #1? Thanks.
vandygrad11
67 is not the only number for #1
we can have several numbers satisfying this condition like 23,32, 12, 21,43,34
also for stmnt 2 any number = or > than 80 will have 8 or 9 as ten's digit which are not prime and don't agree with stmnt 2
(1) the sum of the digits is prime.
We can pick n=83, since 8+3=11 which is prime.
Is 83 < 80? No.
We can also pick 32, since 3+2=5 which is prime.
Is 32 < 80? Yes.
No and Yes, therefore insufficient.
(2) Each of the digits is prime.
Well, that means that each digit is either 2, 3, 5 or 7. In other words, the biggest possible value for n is 77. Therefore, every possible value for n will be less than 80: sufficient.
(1) is insufficient, (2) is sufficient: choose (b).
We can pick n=83, since 8+3=11 which is prime.
Is 83 < 80? No.
We can also pick 32, since 3+2=5 which is prime.
Is 32 < 80? Yes.
No and Yes, therefore insufficient.
(2) Each of the digits is prime.
Well, that means that each digit is either 2, 3, 5 or 7. In other words, the biggest possible value for n is 77. Therefore, every possible value for n will be less than 80: sufficient.
(1) is insufficient, (2) is sufficient: choose (b).
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geometric
If n is an integer between 10 and 99, is n < 80?
(1) The sum of the two digits of n is a prime number.
Lets take numbers:
\(76 - 7 + 6 = 13 =\)Prime \(< 80\)
\(85 - 8 + 5 = 13 =\)Prime \(> 80\)
Hence, (1) ===== is NOT SUFFICIENT
(2) Each of the two digits of n is a prime number.
\(8\) & \(9\) are non prime numbers
Hence, the only possibility of having both the digits as prime is when the number is \(< 80\)
Hence, (2) ===== is SUFFICIENT
Hence, Answer is B
You liked the answer? Appreciate with a Kudos
Hi
Statement 1:
12 ( 1+2 is the prime 3) satisfies smaller than 80
On the other hand 92 ( 9+2 is the prime 11) is bigger than 80. Not sufficient
Statement 2:
If each digit is a prime the tens 8 and 9 are out so it can't be any number grater than 80.
77 ( 7 in the tens and units is prime) is the biggest number which satisfies the statement ( and 75, 73, 72, 57, ,55, 53, 52 etc..)
So it will always be less than 80. Sufficient B
Posted from my mobile device
Statement 1:
12 ( 1+2 is the prime 3) satisfies smaller than 80
On the other hand 92 ( 9+2 is the prime 11) is bigger than 80. Not sufficient
Statement 2:
If each digit is a prime the tens 8 and 9 are out so it can't be any number grater than 80.
77 ( 7 in the tens and units is prime) is the biggest number which satisfies the statement ( and 75, 73, 72, 57, ,55, 53, 52 etc..)
So it will always be less than 80. Sufficient B
Posted from my mobile device
geometric
(1) \(8 + 5 = 13; n > 80\)
\(5 + 8 = 13; n < 80\)
INSUFFICIENT.
(2) This statement tells us that each digit is 2, 3, 5, or 7. We can conclude that \(n < 80\).
SUFFICIENT.
Answer is B.
Posts: 4,849
If n is an integer between 10 and 99, is n < 80?
(1) The sum of the two digits of n is a prime number.
Lets try some numbers: 29 ==> sum of digits = 2+9= 11 is a prime
92 ==>sum of digits = 2+9= 11 is a prime
So we cannot confirm whether n is less than 80 or not.
Hence statement 1 alone is insufficient
(2) Each of the two digits of n is a prime number.
Since 8 and 9 is not a prime number , we can confirm the n will be less than 80.
Statement 2 alone is sufficient.
Option D is the correct answer.
Thanks,
Clifin J Francis
GMAT SME
(1) The sum of the two digits of n is a prime number.
Lets try some numbers: 29 ==> sum of digits = 2+9= 11 is a prime
92 ==>sum of digits = 2+9= 11 is a prime
So we cannot confirm whether n is less than 80 or not.
Hence statement 1 alone is insufficient
(2) Each of the two digits of n is a prime number.
Since 8 and 9 is not a prime number , we can confirm the n will be less than 80.
Statement 2 alone is sufficient.
Option D is the correct answer.
Thanks,
Clifin J Francis
GMAT SME
Hi,
What about the number 93 which is also suitable for statement (2) and in the range from 10 to 99 ?
What about the number 93 which is also suitable for statement (2) and in the range from 10 to 99 ?
Bunuel
Tamnh8
(2) says: Each of the two digits of n is a prime number.
n cannot be 93 because 9 is not a prime number.
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